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A SOLVABLE VERSION OF THE BAER–SUZUKI THEOREM AND
GENERALIZATIONS
by
Simon Guest
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MATHEMATICS)
August 2008
Copyright 2008 Simon Guest

Suppose that G is a finite group and x in G has prime order p > 3. Then x is contained in the solvable radical of G if (and only if) is solvable for all g in G. Also if x has arbitrary order then x is contained in the solvable radical if and only if is solvable for all g1,g2,g3 in G. If G is an almost simple group and x in G has prime order p > 3 then this implies that there exists g in G such that is not solvable. In fact, this is also true when p = 6 and 9 and also with p = 3 with very few exceptions, which are described explicitly.

A SOLVABLE VERSION OF THE BAER–SUZUKI THEOREM AND
GENERALIZATIONS
by
Simon Guest
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MATHEMATICS)
August 2008
Copyright 2008 Simon Guest